I first visited Cuba in 1982, just before the Falklands War broke out. I've always been fascinated with the country - its politics, its music and (because of my bilingual background) its literature.

On that first visit, I made it one of my projects to scour Havana's bookshops for contemporary poetry. I didn't really know what I was looking for, but it certainly wasn't the Marxist-Leninist tomes and Spanish translations of Agatha Christie novels that seemed to form the bulk of the stock. In the poetry section of one store I found a nice translation into Spanish of Mayakovsky's journals, and among contemporary poets Roberto Retamar, Nancy Morejón and Roberto Branly were prominent. I picked up some books but I was slightly disappointed.

I later found out that these poets were literary apparatchiks approved by the regime. They are included in The Whole Island: Six Decades of Cuban Poetry, a magnificent bilingual anthology edited by Mark Weiss and published last year by the University of California Press; but among a bunch of more interesting poets, some with troubled political histories behind them.

I wish I'd had a book like this to refer to back then. I've had to learn about Cuban poetry rather slowly over the years.

The granddaddy of modern Cuban poetry is of course José Martí, who also has a general Father of the Nation distinction for his role as a political leader in Cuba's fight for independence from Spain in the 19th century. On my most recent trip to Cuba, two years ago, I visited his grave in Santiago, which is rather awesomely guarded around the clock by the Cuban army (see below).

José Martí's grave in Santiago de Cuba (my 2008 photo)

Although his name will mean little or nothing to the great British public, there is one tenuous connection: if you've ever heard the chant "One Stevie Gerrard, there's only one Stevie Gerrard" or the like at a football ground, you may know that it's sung to the tune of Cuba's unofficial national song "Guantanamera", whose lyrics are taken from one of Martí's "Versos sencillos" ("Simple verses"). This sequence stands in relation to Martí's major poetic achievement as Blake's "Songs of Innocence and Experience" do to his. The song celebrates a girl from the province of Guantánamo; what an irony that this name is now indelibly associated with the US prison camp disfiguring its southern coast.I had tended to assume because of all this that Martí's poetry was simply a matter of patriotic sentimentality. Not a bit of it: Martí was indeed a major poet as well as an important revolutionary figure, and Mark Weiss's introduction, which you can download here, charts his influence on the later poets included in this 600-page anthology.

The introduction also usefully charts the political ebbing and flowing that has influenced the changing fortunes of many of these poets. The best known incident was the "Padilla affair" - Heberto Padilla, once highly lauded in Cuba, fell foul of the regime and was briefly imprisoned in the 1970s before being allowed to emigrate to the US. A depressingly high proportion of the 55 or so poet included here seem to have fled the island for whatever reasons, ending up in the US, other countries in Latin America or Spain.

Among these, and one of the revelations for me, is José Kozer, whom Weiss has already extensively translated. A Cuban of Jewish origin, Kozer's work, often in long prose lines, is as grotesquely imaginative as Kafka or Bruno Schulz.

You won't find much dutiful propagandist work here; on the contrary, here is much evidence that Cuban poetry has been at the forefront of 20th century innovations, starting with the Aimé Cesaire-like surrealism of Nicolás Guillén (1902-1989). Newcomers to Cuban poetry should immediately check out the great José Lezama Lima and Eliseo Diego, both generously represented. Of the younger poets, I was taken with the linguistic distortions of Carlos A Aguilera (b. 1970), whose "B, CE-" references Gottfried Benn and Paul Celan.

Among the relatively few women, Reina María Rodríguez is important not just as a poet but as the organiser of an influential regular meeting place (her azotea, or rooftop apartment) for artists and writers since the late 1980s.

This is a book I have had at my bedside for many weeks now and have yet to finish exploring. The translations are generally excellent and I have few quibbles. Mark Weiss is currently in the UK doing readings, and will doubtless be talking about the anthology too - catch him at Birkbeck College London (room GO1, Clore Building, 7.30, Wednesday 19 May), and in Leicester on 1 June and Roehampton on 2 June.